Overview
A bone mineral density test can help identify the likelihood of osteoporosis, a disease causing bones to become more fragile and more likely to break.
The result of a bone density test is commonly measured as a z score. The population of z scores is normally distributed with a mean of zero and a standard deviation of one. Therefore these tests meet the requirement of a standard normal distribution and the graph of bone density is a bell-shaped normal distribution curve.
Questions: A randomly selected adult undergoes a bone density test.
Question #1)
Find the probability that this person has a bone density test less than 1.27. Show your work, and explain your solution.
Question #2)
Find the probability that this person has a bone density test of more than 1.27. Show your work, and explain your solution.
Question #3)
Find the probability that this person has a bone density test z = -1. Show your work.
Question #4)
Explain your solution step by step for question #3.